President Trump’s press conference with Russian President Vladimir Putin on Monday has set off a bigger-than-usual backlash, provoking criticism from both the right and the left. It has also presented a quandary for those who work in the Trump administration, who seem unable to guide or influence the president in any real way when it comes to Russia. In the hours afterward, critics have asked a similar question: Given the president’s behavior, should the officials working for him stay, or should they go?

The criticism has centered on Trump siding with Russia over his own intelligence community’s conclusions on election interference, as well as the strange optics of his deference to Putin. For some government workers, his posture is anathema to their goals on Russia policy. “It is horrifying and abhorrent that the president would stand next to arguably our greatest adversary and call into question the work of the intelligence community, which is locked in combat with the Russians on a daily basis,” said a former National Security Council official, who spoke on the condition of anonymity, in a text message. Asked whether those national-security officials serving under Trump should resign, the source said: “Yes on some level I think they should resign, however they did take an oath to defend the constitution from all enemies foreign and domestic. If they resign who is left to try to save things.

“I’ve heard a number of very solid Trump supporters express the same thing,” the former official added. “The same level of disgust.”

Several voices in the commentariat, like Ruth Marcus at The Washington Postand Fred Kaplan at Slate, have called on Trump’s staff to leave in protest. “This is an outright rebuke of the men and women who head his intelligence agencies,” echoed Nicolle Wallace, a former Bush White House official, on her MSNBC show on Monday. “How does [CIA Director] Gina Haspel stay on the job? How does [Director of National Intelligence] Dan Coats stay on the job?”

While this sort of public pressure from nonsupporters doesn’t normally matter much to the Trump administration, high-profile staffers and surrogates have been unusually tight-lipped since the summit ended. That silence might be telling.

“There weren’t a lot of administration officials or White House officials going on TV pushing back and defending the president,” said a former administration official who spoke on the condition of anonymity. This “foretells that this may be a bridge too far for a lot of people. It might be close to the red line.”

The former official said many in the administration have “reservations” about Trump’s stance on Russia, adding, “I do think staffers are hesitant to put themselves out on a limb.” (A White House spokesperson didn’t return a request for comment.)

That’s not to say that people in Trumpworld were necessarily surprised by how the summit went. “I fully expected a train wreck,” said former Trump adviser Sam Nunberg. “Reason being is that one, the legal nuance of Trump having to say, ‘Yes, there was meddling, but no collusion’ is something he’ll never do, because he thinks he’s giving an inch.”

So far, no officials have stepped down in the wake of the summit, and recent history doesn’t point in that direction, despite the resignation question floating around Washington. Hawks like National-Security Adviser John Bolton have stayed in place despite a series of foreign-policy moves that go against their views, including Trump’s diplomacy with North Korea. (Bolton’s spokesman didn’t respond to a request for comment.)

But the distance between how Trump acted in Helsinki and what some of his advisers have called for is hard to reconcile. To name one example: Jon Huntsman, the U.S. ambassador to Russia, said just this past weekend that Russia needed to be “held accountable” for its interference in the election. Yet when asked on Monday whether there’s anything for which he holds Russia accountable, Trump blamed both sides, saying, “Yes, I do. I hold both countries responsible. I think that the United States has been foolish. I think we’ve all been foolish.”

Foreign-policy voices on the right expressed shock at Trump’s comments, but noted that the administration’s policies have, at times, been tougher toward Russia than Trump’s behavior would suggest. Still, “Trump did himself no favors in the press conference feeding fuel to the controversy over U.S.–Russian relations,” said James Carafano, a foreign-policy analyst at the conservative Heritage Foundation. “He may be leaving Putin a genuine ‘off-ramp’ for Russia to change. He has done that with every competitor. But there is virtually no chance Putin will take it … President Trump missed multiple opportunities to hold President Putin accountable on the international stage.”

Mark Dubowitz, the CEO of the Foundation for Defense of Democracies, said Trump’s comments were “contemptuous of his fellow Americans who, on a bipartisan basis, are deeply concerned about Russian belligerence.” But he nevertheless believes that Trump’s staff should stay in place. “They should remain in their jobs to continue implementing a forceful Russia policy that moves the president away from his delusions about Vladimir Putin,” Dubowitz said.

Aside from considerations about duty, there may be more practical matters for aides to weigh, too. “The world doesn’t care when some national-security factotum steps down in high dudgeon,” said Danielle Pletka, a senior vice president at the conservative American Enterprise Institute. “The right thing to do is to ensure that we hold Putin’s feet to the fire in every way—in Ukraine, on corruption, on Georgia, on Nord Stream, on Syria and Iran. If we’re still doing that, my reckoning is that Trump’s people might wish the president was more reticent, but they’re not going to hit the road.”